calculating a sum symbolically

The problem here is to calculate the sum sum_{n>=1} (-1)^(n+1)/(n^2+a) with a some positive real number. You probably all agree that it is preferable to express it using elementary functions from basic calculus as opposed to the Gamma, Zeta and Digamma functions. Well as it turns out it does have a simple expression in terms of the cosecant but Maple does not find it, producing an expression in terms of the Digamma function instead. Mathematica does find the simple formula. So this message goes to the summation algorithm gurus at Maple to suggest they look into this.